FURTHER OBSERVATIONS ON CERTAIN Ufin-TYPE SELECTION PRINCIPLES

We study certain weaker variants of Ufin(𝒪,Ω), namely Ufin(𝒪,ΩD) and Ufin(𝒪,ΩD). We explore many topological properties of Ufin(𝒪,ΩD) and Ufin(𝒪,ΩD). Certain situations are considered when these weaker variants are equivalent to certain related properties. We also make investigations on these variants using critical cardinalities and Alexandroff duplicate. Few observations on productively Ufin(𝒪,ΩD) and productively Ufin(𝒪,ΩD) spaces are presented. Besides, we present certain characterizations of Ufin(𝒪,ΩD) and Ufin(𝒪,ΩD) using weakly groupable covers. We also obtain many game theoretic observations in this context. Some open problems are given.